It could be a GS, but it does sound like he's looking for something to suck. Have you tried a few different kinds of pacifiers? Some babies like a certain brand better than others. The other thing to try would be to give him your finger to suck on instead of the breast to help him settle. He's still so young, so I wouldn't worry about major prop issues, but obviously you don't want him snacking all day either as that won't help get good feeds established.
Also, wrt shh/pat. It's pretty normal for babies of this age to settle with it and then wake right up after being out down. Are you able to continue shh/pat in the crib for 10-15min after you lay him down to help him get into a deeper sleep?